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Functional determinants for Laplacians on annuli and elliptical regions. (English) Zbl 1390.35056

The authors use conformal transformation techniques in order to compute the zeta regularized determinant for ellipsoidal annuli and ellipses. First, the authors discuss the functional determinants between conformally related operators in the plane. The findings are next applied to ellipsoidal annuli and then to ellipses.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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